Is there a machine learning model that can be trained with labels that only say how "right" or "wrong" it was?
What you are looking for is called &quot;reinforcement learning&quot;.
A reinforcement learning algorithm will try to maximize a reward function. This reward represents how &quot;good&quot; or &quot;bad&quot; an action is in the actual context. For example, in the snake game, your reward will be positive for eating an apple and negative when the snake hits a wall.
The interesting thing is that, with reinforcement learning, you can learn without having a reward at each step. In the case of the snake game, your agent can learn that going in the direction of the apple is better than going in the direction of the wall, even if none of this action will directly give a reward (positive or negative).
If you want to use a neural network as your post seem to imply then you should look at deep Q-learning, a reinforcement learning algorithm, which use a neural network to learn to predict the expected reward of a couple (state, action).